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Bilevel stochastic linear programming problems with quantile criterion

  • Stochastic Systems, Queueing Systems
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Abstract

We propose a setting for a bilevel stochastic linear programming problem with quantile criterion. We study continuity properties of the criterial function and prove the existence theorem for a solution. We propose a deterministic equivalent of the problem for the case of a scalar random parameter. We show an equivalent problem in the form of a two-stage stochastic programming problem with equilibrium constraints and quantile criterion. For the case of a discrete distribution of random parameters, the problem reduces to a mixed linear programming problem. We show results of numerical experiments.

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Authors and Affiliations

  1. Moscow Aviation Institute, Moscow, Russia

    S. V. Ivanov

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  1. S. V. Ivanov
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Original Russian Text © S.V. Ivanov, 2014, published in Avtomatika i Telemekhanika, 2014, No. 1, pp. 130–144.

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Ivanov, S.V. Bilevel stochastic linear programming problems with quantile criterion. Autom Remote Control 75, 107–118 (2014). https://doi.org/10.1134/S0005117914010081

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